His Eminence is a historical style of reference for high nobility, still in use in various religious contexts.
A longer, and more formal, title is "His (or Your when addressing the cardinal directly) Most Reverend Eminence". The style for cardinals of noble birth is "His Most Illustrious and Reverend Eminence".
Patriarchs of Eastern Catholic Churches who are also Cardinals may be addressed as "His Eminence" or by the style particular to Eastern Rite Patriarchs, His Beatitude.
When the Grand Master of the Military Order of the Knights of Malta, the Head of state of their sovereign territorial state comprising the island of Malta until 1797, who had already been made a Reichsfürst (i.e. Prince of the Holy Roman Empire) in 1607, was granted ecclesiastical equality with the Cardinals in 1630, he was also awarded the hybrid style His Most Eminent Highness.
While the term is shunned by many individuals of other faiths or denominations of Christianity, the title is officially maintained in international diplomacy without regard for its doctrinal, philosophical and theological origins.